Symmetry SO Research Articles

Kl3form factors

The decay form factors f/sub plus-or-minus/(t) for the process K/sup + -/ ..-->.. ..pi../sup 0/l/sup + -/..nu../sub l/(nu-bar/sub l/) have been evaluated in closed form within the framework of the rest-frame relativistic symmetry SO(4,2) x SU(3) x SU(3). Symmetry breaking is introduced via Lorentz boosting. The resulting explicit expressions and conclusions are in agreement with experiment and contain, in a unified and general manner, the successful results obtained in various other models based on current algebra, Kemmer fields, S-matrix analysis, and algebraic methods.

Lines of fixed points and physically irreducible representations

We will prove that if the order parameter belongs to the representation $D$ which is the direct sum of two complex conjugate irreducible representations, $D=\ensuremath{\Delta}\ensuremath{\bigoplus}{\ensuremath{\Delta}}^{*}$, and if $\ensuremath{\Delta}$ has at least one quartic invariant, then the symmetry SO(2) appears in the parameter space. If, in addition, $\ensuremath{\Delta}$ and ${\ensuremath{\Delta}}^{*}$ are quasiequivalent then higher symmetry than SO(2) will appear in the parameter space. Since SO(2) is a continuous group, every fixed point of the renormalization-group transformations will be either invariant under SO(2) or part of a fixed line generated by SO(2) transformations on the fixed point.

Symmetry breaking and the gravitational field

A model of the gravitational field based on the spontaneously broken local gauge symmetry SO(3, 1) is presented. It is shown that, in contrast with the usual situation, the Higgs mechanism produces a kinetic term in the Lagrangian which, in the weak-static-field limit, yields the gravitational field equation in the Newtonian approximation. Thus a gravitational theory is obtained without the explicit introduction of a gravitational Lagrangian.